Methods of this type are known, for example, from the article “Numerische Simulation der Wärmeleitung in Stahlblechen—Mathematik hilft bei der Steuerung von Kühlstrecken” [Numerical Simulation of the Heat Conduction in Steel Sheets—Mathematics helps to control cooling sections] by W. Borchers et al., published in Unikurier der Friedrich-Alexander-Universität Erlangen-Nürnberg, Volume 102, October 2001, 27th edition.
The known methods are used in particular to control coolant actuators in rolling mills. The coolant actuators may be arranged between the rolling stands. They may also be arranged downstream of the rolling stands. However, there are also other conceivable applications, for example in the context of calculating solidification processes in continuous casting or in the control of rolling mills per se.
In the prior art, the Scheil rule or the Johnson-Mehl-Avrami or Brimacombe approaches are used to determine the proportions of the phases.
The approaches used in the prior art in practice are not without faults in all cases. In particular, they have a range of systematic drawbacks. Firstly, each material has to be parameterized separately. Interpolations between different materials are not possible or at least are only possible to a limited extent. Secondly, the methods of the prior art consider only two phases. The system cannot be expanded to cover more than two phases. Thirdly, the methods of the prior art only provide good correspondence between model and reality if the metal under consideration is completely transformed. Fourthly, the method of the prior art does not give any information about the transformation heat released during the phase transformation. However, knowledge of the transformation heat is imperative if the heat conduction equation is to be correctly solved.